GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
N-30D, 1994-09-27
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LETTER TO SHAREHOLDERS
Dear Shareholder:
    We are pleased to provide you with this annual report for the General
California Municipal Money Market Fund. For the period ended July 31, 1994,
the yield provided by your Fund was 2.25%. The effective yield was 2.27%
after taking into account the effect of compounding.* Income dividends of
approximately $.02 per share paid during the period were exempt from Federal
and State of California personal income taxes.**
    Over the past few months, we have been keeping a watchful eye on the
status of the U.S. economy, the direction of interest rates and any
significant variation in inflationary indicators. Early in the reporting
period, economic numbers hinted that the nation's growth might be more anemic
than anticipated. With no strong threat of a rekindling of inflation, the
municipal market responded with strength, providing some of the lowest
historical yields in both the bond and money markets. In a somewhat unusual
turn of events, assets of municipal money market funds increased despite the
unprecedented low yield environment.
    In the first half of 1994, however, signs of economic strength began to
emerge along with the specter of a tighter Federal Reserve Board policy.
Through a series of tightening moves between February 4 and May 17, the Fed
signaled its desire to choke off inflationary pressures before they had an
opportunity to build significantly. In a step-by-step process which began in
February, the Fed inched up the Federal Funds rate by 175 basis points to the
4 3/4% level. The most overt move came on May 17 when the Fed raised both the
discount rate and the Federal Funds rate by 50 basis points, to 3.50% and
4.25%, respectively: those moves were followed by another 50 basis point
increase earlier this month. The moves appeared to achieve a neutral monetary
policy, clearly signaling the end of the Federal Reserve's 1993 accommodative
stance.
    With these earlier changes in the Federal Reserve's monetary stance, the
unease in other markets served to bolster rates in the short-term municipal
market as cash moved into municipal money markets from both equities and bond
funds. Total net assets of tax exempt money market funds reached an all-time
high of over $119 billion, which declined as tax season arrived.
Traditionally, some municipal money markets lose assets during this time as
investors tap their money funds to pay income taxes. During this period,
municipal notes continued to provide attractive returns compared to taxable
alternatives. Your Fund's yield has remained attractive to the investor
seeking tax exempt income, and the hike in tax rates which took place last
year has made these returns even more attractive on an after-tax basis.
    In recent weeks, many issuers returned to the marketplace with their
traditional summer financings. In addition to the $7 billion of notes issued
by the State of California, various smaller California issuers came to the
short-term market. The increased overall supply of available investments in
the short-term market once again placed upward pressure on yields as supply
outstripped demand. We extended the average maturity of your portfolio to
lock in the attractive yields prevailing in the short-term market at that
time. We will continue to adjust our strategy, when necessary, to respond to
changes in the market, in Federal Reserve policy, and to the proposed changes
in the regulations governing tax exempt money market funds which we have
received from the Securities and Exchange Commission. It is our goal to take
advantage of any market shifts to help your Fund continue to provide one of
the best returns available among California tax exempt money market funds.
    We have included a current Statement of Investments and recent financial
statements for your review and look forward to serving your investment needs
in the future.
                              Very truly yours,

                              (signature logo)
                              Richard J. Moynihan
                              Director, Municipal Portfolio Management
                              The Dreyfus Corporation
August 26, 1994
New York, N.Y.
* Effective yield is based upon dividends declared daily and reinvested
monthly.
** Some income may be subject to the Federal Alternative Minimum Tax (AMT)
for certain shareholders.

<TABLE>
<CAPTION>
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS                                                                               JULY 31, 1994
                                                                                            PRINCIPAL
TAX EXEMPT INVESTMENTS_100.0%                                                                AMOUNT            VALUE
                                                                                         --------------       -------------
<S>                                                                                       <C>                 <C>
Anaheim Housing Authority, MFHR, VRDN:
    (Bel Age Project) 3%, Series A (LOC; Federal Home Loan Banks) (a,b).....              $   5,300,000       $   5,300,000
    Refunding (Villas At Anaheim Hill) 2.85% (LOC; National Bank of Canada) (a,b)             8,850,000           8,850,000
Burbank Redevelopment Agency, Multi-Family Revenue, VRDN
    2.60% (LOC; Coast Savings and Loan) (a,b)...............................                 15,400,000          15,400,000
State of California, RAW 3.75%, 12/21/94....................................                 15,000,000          15,042,671
California Health Facilities Financing Authority, Revenue, VRDN:
    Refunding (Saint Josephs Health Services) 2.65%, Series A (a)...........                  2,585,000           2,585,000
    (Scripps Memorial Hospital) 2.90%, Series B (Insured; MBIA) (a).........                 12,000,000          12,000,000
California Pollution Control Financing Authority:
    PCR:
      CP (Refunding-Pacific Gas and Electric):
          3.25%, Series A, 8/11/94 (LOC; Swiss Bank Corp.) (b)..............                 22,995,000          22,995,000
          3.15%, Series D, 8/18/94 (LOC; Bank of Tokyo) (b).................                  5,000,000           5,000,000
      VRDN;
          (Refunding-Shell Oil Co.) 2.60% (Corp. Guaranty; Shell Oil Co.) (a)                 4,800,000           4,800,000
    RRR, VRDN:
      (Delano Project) 2.60% (LOC; ABN-Amro Bank) (a,b).....................                 23,300,000          23,300,000
      (Honey Lake Power Co. Project) 2.60% (LOC; Banque Nationale de Paris) (a,b)            15,100,000          15,100,000
      Refunding:
          (Ultra Power Malaga Project) 2.65%, Series A (LOC; Bank of America) (a,b)           5,300,000           5,300,000
          (Ultra Power Rocklin Project):
            2.65%, Series A (LOC; Bank of America) (a,b)....................                 16,400,000          16,400,000
            2.65%, Series B (LOC; Bank of America) (a,b)....................                  3,900,000           3,900,000
California School Cash Reserve Program Authority 4.50%, Series A, 7/5/95....                 11,000,000          11,073,545
California Statewide Community Development Authority, TRAN
    4.50%, Series A, 7/17/95................................................                 23,000,000          23,162,545
Concord, MFMR, VRDN:
    (Arcadian Apartments) 2.85%, Series A (LOC; Federal Home Loan Banks) (a,b)                6,000,000           6,000,000
    (Crossroads Apartments) 2.85%, Series B (LOC; Federal Home Loan Banks) (a,b)              3,500,000           3,500,000
Contra Costa County, MFMR, VRDN (El Cerrito Royale Project)
    2.90%, Series A (LOC; Bank of America) (a,b)............................                  1,745,000           1,745,000
Foothill Eastern Transportation Corridor Agency, Toll Road Revenue, VRDN
    2.65% (LOC; Morgan Guaranty Trust Co.) (a,b)............................                 19,500,000          19,500,000
Garden Grove Housing Authority, Multi-Family Revenue, VRDN
    (Valley View Senior Villas Project) 3.25%, Series A (LOC; Wells Fargo Bank) (a,b)         1,600,000           1,600,000
Huntington Beach, MFHR, VRDN:
    (Five Points Seniors Project) 3.25%, Series A (LOC; Wells Fargo Bank) (a,b)               3,100,000           3,100,000
    (Mercury Savings and Loan Village)
      3.20%, Series A (LOC; Resolution Funding Corp.) (a,b).................                  6,000,000           6,000,000
Irvine Ranch Water District, VRDN 2.70%, Series A (LOC; Sumitomo Bank) (a,b)                  1,000,000           1,000,000
Irwindale, IDR, VRDN (Toys "R" Us Inc. Project) 3.025% (LOC; Bankers Trust) (a,b)             3,000,000           3,000,000

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS (CONTINUED)                                                                 JULY 31, 1994
                                                                                            PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                            AMOUNT              VALUE
                                                                                         --------------       -------------

Kern County, COP, VRDN (Kern Public Facilities Project)
    2.70%, Series B (LOC; Sanwa Bank) (a,b).................................             $   13,900,000      $   13,900,000
Loma Linda, VRDN:
    HR (Loma Linda University Medical Center):
      2.70%, Series C (LOC; Industrial Bank of Japan) (a,b).................                 13,065,000          13,065,000
      2.85%, Series C (LOC; Industrial Bank of Japan) (a,b).................                  5,000,000           5,000,000
    MFHR, VRDN (Loma Linda Springs Apartment) 3.65% (LOC; Tokai Bank) (a,b).                  3,930,000           3,930,000
Los Angeles, MFHR, VRDN:
    (Beverly Park Apartments) 2.75%, Series A (LOC; Barclays Bank) (a,b)....                  7,600,000           7,600,000
    (Studio Colony Project) 2.90%, Series C (LOC; Industrial Bank of Japan) (a,b)             9,795,000           9,795,000
Los Angeles Community Redevelopment Agency, MFHR, VRDN:
    (Grand Promenade Project) 3.45% (LOC; Tokai Bank) (a,b).................                  7,900,000           7,900,000
    (Rental Academy Apartments) 3.20%, Series A (LOC; Dai-Ichi Kangyo Bank) (a,b)             6,300,000           6,300,000
Los Angeles County, TRAN 4.50%, 6/30/95.....................................                 13,710,000          13,788,265
Los Angeles County Department of Water and Power, CP 3.20%, 8/16/94.........                  8,750,000           8,750,000
Los Angeles County Housing Authority, MFHR, VRDN:
    (Malibu Canyon Apartments) 2.80%, Series B (LOC; Coast Savings and Loan) (a,b)            9,300,000           9,300,000
    (River Park Apartment Project) 3.05%, Series D (LOC; Dai-Ichi Kangyo Bank) (a,b)          5,000,000           5,000,000
Los Angeles County Industrial Development Authority, IDR, VRDN (Fruitland
Association)
    4%, Issue II (LOC; Tokai Bank) (a,b)....................................                  3,600,000           3,600,000
Los Angeles County Local Educational Agencies, COP, TRAN 4.50%, 7/6/95......                  8,000,000           8,053,644
Los Angeles County Metropolitan Transportation Authority:
    Revenue, RAN 3.75%, Series A, 3/14/95 (LOC; Union Bank of Switzerland) (b)               14,000,000          14,037,558
    Sales Tax Revenue, Refunding, VRDN (Property C)
      2.65%, Series A (Insured; MBIA and SBPA; Industrial Bank of Japan) (a)                 29,000,000          29,000,000
Los Angeles County Transportation Community, Sales Tax Revenue, CP
    3.10%, Series A 10/19/94 (LOC: ABN-Amro Bank, Banco Nationale de Paris,
Bank of
    California, Canadian Imperial Bank of Commerce and National Westminster Bank) (b)        10,000,000          10,000,000
Los Angeles Harbor Department, Revenue, VRDN (Wilmington Liquid Terminals
Inc.)
    3% (LOC; The Bank of New York) (a,b)....................................                 25,000,000          25,000,000
Los Angeles Unified School District, TRAN 4.50%, 7/10/95....................                 10,875,000          10,963,716
City of Oceanside, MFMR, VRDN (Riverview Springs Apartments)
    3.05%, Series A (LOC; Bank of Tokyo) (a,b)..............................                  3,820,000           3,820,000
Orange County Various Sanitation Districts, COP, Refunding, VRDN
    2.65% (Insured; FGIC) (a,b).............................................                    100,000             100,000
City of Oxnard Housing Authority, MFHR, VRDN (Seawind Apartments Project)
    2.95%, Series A (LOC; Federal Home Loan Banks) (a,b)....................                  2,400,000           2,400,000
Palm Springs Industrial Development Authority, Revenue, VRDN (BP Holdings
Project)
    2.95%, Series A (LOC; First Interstate Bank of California) (a,b)........                  5,200,000           5,200,000
Paramount, MFHR, VRDN:
    (Mercury Savings and Loan Triangle Development Project)
      3.20%, Series A (LOC; Resolution Funding Corp.) (a,b).................                  9,000,000           9,000,000
    (Twin Towers Apartments Project) 3% (LOC; Federal Home Loan Banks) (a,b)                  8,700,000           8,700,000

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS (CONTINUED)                                                                    JULY 31, 1994
                                                                                            PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                            AMOUNT            VALUE
                                                                                         --------------       -------------
Pleasant Hill, MFMR, VRDN (Brookside Apartments)
    2.85%, Series A (LOC; Federal Home Loan Banks) (a,b)....................            $     2,200,000      $    2,200,000
Redlands, MFHR, VRDN, Refunding (Parkview Terrace)
    2.75%, Series A (LOC; Bank of America) (a,b)............................                 10,000,000          10,000,000
Riverside, MFHR, VRDN (Crest Apartments Project)
    3.45%, Series A (LOC; Tokai Bank) (a,b).................................                  3,500,000           3,500,000
Riverside County, TRAN 4.25%, 6/30/95.......................................                 10,000,000          10,057,177
Riverside County Housing Authority, VRDN:
    MFHR:
      (Tyler Village Project) 3.65%, Series A (LOC; Tokai Bank) (a,b).......                  3,355,000           3,355,000
      (Victoria Springs Apartments) 3.05% (LOC; Bank of America) (a,b)......                  6,300,000           6,300,000
    MFMR (Emeritus Park) 2.85%, Series B (LOC; Federal Home Loan Banks) (a,b)                 3,850,000           3,850,000
Riverside County School Financing Authority, RAN (School District Financing)
    4.50%, 7/7/95...........................................................                 23,100,000          23,276,340
Sacramento County, VRDN:
    COP (Administration Center and Court House Project)
      2.70% (LOC; Union Bank of Switzerland) (a,b)..........................                  5,000,000           5,000,000
    MFHR:
      3.05%, Series A (LOC; Dai-Ichi Kangyo Bank) (a,b).....................                  7,900,000           7,900,000
      3.05%, Series C (LOC; Dai-Ichi Kangyo Bank) (a,b).....................                  2,400,000           2,400,000
      Refunding (Smoketree Apartments) 2.85% (LOC; Federal Home Loan Banks) (a,b)             3,900,000           3,900,000
Sacramento County Housing Authority, MFHR, VRDN:
    Refunding (Grouse Run Apartments) 2.75% (LOC; Bank of America) (a,b)....                  2,400,000           2,400,000
    (Stone Creek Apartments Project) 3.10%, Series L
      (LOC; First Interstate Bank of California) (a,b)......................                  5,450,000           5,450,000
San Bernardino Board of Education, TRAN 4.25%, 7/28/95......................                 10,000,000          10,027,518
San Bernardino County, VRDN:
    COP 3.05% (LOC; Sumitomo Trust and Banking Co.) (a,b)...................                 12,000,000          12,000,000
    MFHR:
      (Meadowland Apartments Project)
          2.90%, Series A (LOC; Bayerische Landesbank Girozentrale) (a,b)...                  8,000,000           8,000,000
      Refunding (Park Heights Apartments) 3.10% (LOC; Federal Home Loan Banks) (a,b)          5,520,000           5,520,000
City of San Diego, MFHR, Refunding, VRDN (University Town Center Apartments)
    2.75% (LOC; Bank of America) (a,b)......................................                  7,000,000           7,000,000
San Diego Area Local Government, COP, TRAN 4.50%, 6/30/95...................                 15,000,000          15,115,344
San Diego County Regional Transportation Commission, Sales Tax Revenue, VRDN
    2.85%, (Insured; FGIC) (a)..............................................                  6,000,000           6,000,000
San Diego Housing Authority, MFHR, VRDN (Nobel Court Apartments)
    2.80% (LOC; Citibank) (a,b).............................................                  4,000,000           4,000,000
San Dimas Redevelopment Agency Industrial Development Authority, IDR, VRDN
    (French Co. Project) 3.20% (LOC; Credit Commercial de France) (a,b).....                  4,600,000           4,600,000

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS (CONTINUED)                                                                     JULY 31, 1994
                                                                                            PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                            AMOUNT            VALUE
                                                                                         --------------       -------------
San Francisco City and County Redevelopment Agency, Multi-Family Revenue,
VRDN
    (Bayside Village Project):
      2.80%, Series A (LOC; Industrial Bank of Japan) (a,b).................            $     2,500,000     $     2,500,000
      2.80%, Series B (LOC; Industrial Bank of Japan) (a,b).................                  7,600,000           7,600,000
San Francisco City and County Unified School District, TRAN 3.50%, 8/12/94..                  8,000,000           8,001,052
Santa Ana Housing Authority, MFHR, VRDN (Vintage Apartments Project)
    3.65%, Series A (LOC; Tokai Bank) (a,b).................................                  4,225,000           4,225,000
Santa Clara, Electric Revenue, VRDN (Junior Lien)
    2.75%, Series B (LOC; National Westminster Bank) (a,b)..................                  3,400,000           3,400,000
Santa Clara County Transportation District, Refunding, VRDN
    2.60%, Series 85A (LOC; Sumitomo Bank) (a,b)............................                  1,600,000           1,600,000
Simi Valley, MFHR, Refunding, VRDN 2.80%, Series A (LOC; Bank of America) (a,b)              12,070,000          12,070,000
Southern California Public Power Authority, Transmission Project Revenue,
Refunding
    VRDN (Southern Transmission)
    2.70% (Insured; AMBAC and LOC; Swiss Bank Corp.) (a,b)..................                 15,600,000          15,600,000
                                                                                                                 ----------
TOTAL INVESTMENTS (cost $686,704,375).......................................                                  $ 686,704,375
                                                                                                              =============
</TABLE>
<TABLE>
<CAPTION>
SUMMARY OF ABBREVIATIONS
<S>           <C>                                                <S>     <C>
AMBAC         American Municipal Bond Assurance Corporation      MFMR    Multi-Family Mortgage Revenue
COP           Certificate of Participation                       PCR     Pollution Control Revenue
CP            Commercial Paper                                   RAN     Revenue Anticipation Notes
FGIC          Financial Guaranty Insurance Corporation           RAW     Revenue Anticipation Warrants
HR            Hospital Revenue                                   RRR     Resources Recovery Revenue
IDR           Industrial Development Revenue                     SBPA    Standby Bond Purchase Agreement
LOC           Letter of Credit                                   TRAN    Tax and Revenue Anticipation Notes
MBIA          Municipal Bond Insurance Association               VRDN    Variable Rate Demand Notes
MFHR          Multi-Family Housing Revenue
</TABLE>


SUMMARY OF COMBINED RATINGS (UNAUDITED)
MOODY'S              OR        STANDARD & POOR'S           PERCENTAGE OF VALUE
- -------                       ------------------           -------------------
VMIG1/MIG1, P1 (c)             SP1+/SP1, A1+/A1 (c)                 91.0%
VMIG2/MIG2, P2                 SP2, A2                               2.4
Aaa/Aa (d)                     AAA/AA (d)                            5.5
Not Rated (e)                  Not Rated (e)                         1.1
                                                                   ------
                                                                   100.0%
                                                                   ======

NOTES TO STATEMENT OF INVESTMENT:
    (a)  Securities payable on demand. The interest rate, which is subject to
    change, is based upon bank prime rates or an index of market interest
    rates.
    (b)  Secured by letters of credit. At July 31, 1994, 67.9% of the Fund's
    net assets are backed by letters of credit issued by domestic banks and
    foreign banks.
    (c)  P1 and A1 are the highest ratings assigned tax-exempt commercial
    paper by Moody's and Standard & Poor's, respectively.
    (d)  Notes which are not MIG or SP rated are represented by bond ratings
    of the issuers.
    (e)  Securities which, while not rated by Moody's and Standard & Poor's,
    respectively, have been determined by the Fund's Board of Trustees to be
    of comparable quality to those rated securities in which the Fund may
    invest.
    (f)  At July 31, 1994, the Fund had $227,410,000 (32.5% of net assets)
    invested in securities whose payment of principal and interest is
    dependent upon revenues generated from housing projects.
    See notes to financial statements.

<TABLE>
<CAPTION>
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF ASSETS AND LIABILITIES                                                                JULY 31, 1994
<S>                                                                                         <C>                <C>
ASSETS:
    Investments in securities, at value-Note 1(a)...........................                                   $686,704,375
    Cash....................................................................                                      9,926,428
    Interest receivable.....................................................                                      2,807,363
    Prepaid expenses........................................................                                         41,545
                                                                                                               ------------
                                                                                                                699,479,711
LIABILITIES:
    Due to The Dreyfus Corporation..........................................                $   148,937
    Accrued expenses and other liabilities..................................                    225,795             374,732
                                                                                            -----------        ------------
NET ASSETS  ................................................................                                   $699,104,979
                                                                                                               ============
REPRESENTED BY:
    Paid-in capital.........................................................                                   $699,224,635
    Accumulated net realized (loss) on investments..........................                                       (119,656)
                                                                                                               ------------
NET ASSETS at value applicable to 699,224,635 shares outstanding
    (unlimited number of $.001 par value shares of
    Beneficial Interest authorized).........................................                                   $699,104,979
                                                                                                               ============
NET ASSET VALUE, offering and redemption price per share
    ($699,104,979 / 699,224,635 shares).....................................                                          $1.00
                                                                                                                      =====

STATEMENT OF OPERATIONS                                                                        YEAR ENDED JULY 31, 1994
INVESTMENT INCOME:
    INTEREST INCOME.........................................................                                  $  17,903,061
    EXPENSES:
      Management fee-Note 2(a).............................................                  $3,474,588
      Shareholder servicing costs-Note 2(c).................................                    592,752
      Custodian fees........................................................                     62,272
      Professional fees.....................................................                     52,770
      Registration fees.....................................................                     33,033
      Prospectus and shareholders' reports-Note 2(b)........................                     25,478
      Trustees' fees and expenses-Note 2(d).................................                     18,932
      Miscellaneous.........................................................                     22,172
                                                                                             ----------
                                                                                              4,281,997
      Less_reduction in management fee due to
          undertakings-Note 2(a)............................................                  1,968,729
                                                                                             ----------
            TOTAL EXPENSES..................................................                                      2,313,268
                                                                                                                  ---------
INVESTMENT INCOME-NET......................................................                                      15,589,793
NET REALIZED (LOSS) ON INVESTMENTS..........................................                                       (111,389)
                                                                                                                  ---------
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                                  $  15,478,404
                                                                                                              =============
See notes to financial statements.
</TABLE>

<TABLE>
<CAPTION>
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF CHANGES IN NET ASSETS
                                                                                           YEAR ENDED JULY 31,
                                                                                       ----------------------------------
                                                                                              1993              1994
                                                                                        --------------    ---------------
<S>                                                                                    <C>                     <C>
OPERATIONS:
    Investment income-net..................................................            $     14,833,228        $ 15,589,793
    Net realized (loss) on investments......................................                    (8,267)            (111,389)
                                                                                        --------------      ---------------
      NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS..................                 14,824,961          15,478,404
                                                                                        --------------      ---------------
DIVIDENDS TO SHAREHOLDERS FROM:
    Investment income-net..................................................                (14,833,228)         (15,589,793)
    Net realized gain on investments........................................                    (4,534)             --
                                                                                        --------------      ---------------
      TOTAL DIVIDENDS.......................................................               (14,837,762)         (15,589,793)
                                                                                        --------------      ---------------
BENEFICIAL INTEREST TRANSACTIONS ($1.00 per share):
    Net proceeds from shares sold...........................................              1,580,032,863       2,518,641,419
    Dividends reinvested....................................................                 13,832,655          14,582,815
    Cost of shares redeemed.................................................             (1,534,701,903)     (2,442,541,575)
                                                                                        --------------      ---------------
      INCREASE IN NET ASSETS FROM BENEFICIAL INTEREST TRANSACTIONS..........                 59,163,615          90,682,659
                                                                                        --------------      ---------------
          TOTAL INCREASE IN NET ASSETS......................................                 59,150,814          90,571,270
NET ASSETS:
    Beginning of year.......................................................                549,382,895         608,533,709
                                                                                        --------------      ---------------
    End of year.............................................................            $   608,533,709     $   699,104,979
                                                                                        ==============      ===============
                   See notes to financial statements.

</TABLE>

<TABLE>
<CAPTION>
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
FINANCIAL HIGHLIGHTS
    Contained below is per share operating performance data for a share of
Beneficial Interest outstanding, total investment return, ratios to average
net assets and other supplemental data for each year indicated. This
information has been derived from the Fund's financial statements.
                                                                                YEAR ENDED JULY 31,
                                                                --------------------------------------------------------
PER SHARE DATA:                                                     1990        1991        1992        1993        1994
                                                                ----------   --------   -----------   -------   --------
    <S>                                                         <C>         <C>           <C>         <C>        <C>
    Net asset value, beginning of year..............            $  .9992    $  .9996      $1.0000     $1.0000    $1.0000
                                                                -------     -------       ------      ------     -------
    INVESTMENT OPERATIONS:
    Investment income_net..........................                .0578       .0517        .0359       .0243      .0225
    Net realized gain (loss) on investments.........               .0004       .0004         --          --       (.0002)
                                                                 -------     -------       ------      ------     -------
      TOTAL FROM INVESTMENT OPERATIONS..............               .0582       .0521        .0359       .0243      .0223
                                                                 -------     -------       ------      ------     -------
    DISTRIBUTIONS:
    Dividends from investment income_net...........               (.0578)     (.0517)      (.0359)     (.0243)    (.0225)
    Dividends from net realized gain on investments.               --           --           --          --          --
                                                                -------       -------      ------      ------     -------
      TOTAL DISTRIBUTIONS...........................              (.0578)     (.0517)      (.0359)     (.0243)    (.0225)
                                                                -------       -------      ------      ------     -------
    Net asset value, end of year....................            $  .9996     $1.0000      $1.0000     $1.0000    $ .9998
                                                                 =======      =======     =======      =======    ========
TOTAL INVESTMENT RETURN                                           5.93%       5.29%        3.65%       2.46%      2.27%
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets.........               .07%        .02%         .20%        .33%       .33%
    Ratio of net investment income to average net
      assets.......................................               5.78%       5.08%        3.59%       2.43%      2.24%
    Decrease reflected in above expense ratios due
      to undertakings by the Manager................               .65%        .59%         .41%        .30%       .28%
    Net Assets, end of year (000's Omitted).........             $281,909   $538,978     $549,383    $608,534   $699,105

                    See notes to financial statements.
</TABLE>

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
NOTES TO FINANCIAL STATEMENTS
NOTE 1-SIGNIFICANT ACCOUNTING POLICIES:
    The Fund is registered under the Investment Company Act of 1940 ("Act")
as a non-diversified open-end management investment company. Dreyfus Service
Corporation acted as the distributor of the Fund's shares until August 24,
1994, which are sold to the public without a sales load. Dreyfus Service
Corporation is a wholly-owned subsidiary of The Dreyfus Corporation
("Manager"). Effective August 24, 1994, the Manager became a direct
subsidiary of Mellon Bank, N.A.
    On August 24, 1994, Premier Mutual Fund Services Inc. ("Premier") was
engaged as the Fund's distributor. Premier, located at One Exchange Place,
Boston, Massachusetts 02109, is a wholly-owned subsidiary of Institutional
Administration Services, Inc., a provider of mutual fund administration
services, the parent company of which is Boston Institutional Group, Inc.
    It is the Fund's policy to maintain a continuous net asset value per
share of $1.00; the Fund has adopted certain investment, portfolio valuation
and dividend and distribution policies to enable it to do so.
    (A) PORTFOLIO VALUATION: Investments are valued at amortized cost, which
has been determined by the Fund's Board of Trustees to represent the fair
value of the Fund's investments.
    (B) SECURITIES TRANSACTIONS AND INVESTMENT INCOME: Securities
transactions are recorded on a trade date basis. Interest income, adjusted
for amortization of premiums and original issue discounts on investments, is
earned from settlement date and recognized on the accrual basis. Realized
gain and loss from securities transactions are recorded on the identified
cost basis.
    The Fund follows an investment policy of investing primarily in municipal
obligations of one state. Economic changes affecting the state and certain of
its public bodies and municipalities may affect the ability of issuers within
the state to pay interest on, or repay principal of, municipal obligations
held by the Fund.
    (C) DIVIDENDS TO SHAREHOLDERS: It is the policy of the Fund to declare
dividends daily from investment income-net. Such dividends are paid monthly.
Dividends from net realized capital gain, if any, are normally declared and
paid annually, but the Fund may make distributions on a more frequent basis
to comply with the distribution requirements of the Internal Revenue Code. To
the extent that net realized capital gain can be offset by capital loss
carryovers, it is the policy of the Fund not to distribute such gain.
    (D) FEDERAL INCOME TAXES: It is the policy of the Fund to continue to
qualify as a regulated investment company, which can distribute tax exempt
dividends, by complying with the applicable provisions of the Internal
Revenue Code, and to make distributions of income and net realized capital
gain sufficient to relieve it from substantially all Federal income taxes.
    The Fund has an unused capital loss carryover of approximately $8,200
available for Federal income tax purposes to be applied against future net
securities profits, if any realized subsequent to July 31, 1994. The
carryover does not include net realized securities losses from November 1,
1993 through July 31, 1994 which are treated, for Federal income tax
purposes, as arising in fiscal 1995. If not applied, the carryover expires in
fiscal 2002.
    At July 31, 1994, the cost of investments for Federal income tax purposes
was substantially the same as the cost for financial reporting purposes (see
the Statement of Investments).
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
NOTE 2_MANAGEMENT FEE AND OTHER TRANSACTIONS WITH AFFILIATES:
    (A) Pursuant to a management agreement ("Agreement") with the Manager,
the management fee is computed at the annual rate of .50 of 1% of the average
daily value of the Fund's net assets and is payable monthly. The Agreement
provides for an expense reimbursement from the Manager should the Fund's
aggregate expenses, exclusive of taxes, brokerage, interest on borrowings and
extraordinary expenses, exceed 1 1/2% of the average value of the Fund's net
assets for any full fiscal year. However, during the year ended July 31,
1994, the Manager had undertaken to reduce the management fee paid by the
Fund, to the extent that the Fund's aggregate expenses exceeded specified
annual percentages of the Fund's average daily net assets. The reduction in
management fee, pursuant to the undertaking, amounted to $1,968,729 for the
year ended July 31, 1994.
    The Manager may modify the expense limitation percentages from time to
time, provided that the resulting expense reimbursement would not be less
than the amount required pursuant to the Agreement.
    (B) The Fund has adopted a Service Plan (the "Plan") pursuant to which
the Fund will bear the costs of preparing, printing and distributing certain
of the Fund's prospectuses and statements of additional information and costs
associated with implementing and operating the Plan, not to exceed the
greater of $100,000 or .005 of 1% of the Fund's average daily net assets for
any full fiscal year. For the year ended July 31, 1994, the Fund was charged
$11,231 pursuant to the Plan.
    (C) Pursuant to the Fund's Shareholder Services Plan, the Fund reimburses
Dreyfus Service Corporation an amount not to exceed an annual rate of .25 of
1% of the value of the Fund's average daily net assets for servicing
shareholder accounts. The services provided may include personal services
relating to shareholder accounts, such as answering shareholder inquiries
regarding the Fund and providing reports and other information, and services
related to the maintenance of shareholder accounts. During the year ended
July 31, 1994, the Fund was charged an aggregate of $226,917 pursuant to the
Shareholder Services Plan.
    (D) Certain officers and trustees of the Fund are "affiliated persons,"
as defined in the Act, of the Manager and/or Dreyfus Service Corporation.
Each trustee who is not an "affiliated person" receives an annual fee of
$2,500 and an attendance fee of $250 per meeting.

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
REPORT OF ERNST & YOUNG LLP, INDEPENDENT AUDITORS
SHAREHOLDERS AND BOARD OF TRUSTEES
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
    We have audited the accompanying statement of assets and liabilities of
General California Municipal Money Market Fund, including the statement of
investments, as of July 31, 1994, and the related statement of operations for
the year then ended, the statement of changes in net assets for each of the
two years in the period then ended and financial highlights for each of the
years indicated therein. These financial statements and financial highlights
are the responsibility of the Fund's management. Our responsibility is to
express an opinion on these financial statements and financial highlights
based on our audits.
    We conducted our audits in accordance with generally accepted auditing
standards. Those standards require that we plan and perform the audit to
obtain reasonable assurance about whether the financial statements and
financial highlights are free of material misstatement. An audit includes
examining, on a test basis, evidence supporting the amounts and disclosures
in the financial statements. Our procedures included confirmation of
securities owned as of July 31, 1994 by correspondence with the custodian. An
audit also includes assessing the accounting principles used and significant
estimates made by management, as well as evaluating the overall financial
statement presentation. We believe that our audits provide a reasonable basis
for our opinion.
    In our opinion, the financial statements and financial highlights
referred to above present fairly, in all material respects, the financial
position of General California Municipal Money Market Fund at July 31, 1994,
the results of its operations for the year then ended, the changes in its net
assets for each of the two years in the period then ended, and the financial
highlights for each of the indicated years, in conformity with generally
accepted accounting principles.



(signature logo)
New York, New York
September 6, 1994


IMPORTANT TAX INFORMATION (UNAUDITED)
    In accordance with Federal tax law, the Fund hereby designates all the
dividends paid from investment income-net during the fiscal year ended July
31, 1994 as "exempt-interest dividends" (not subject to regular Federal and,
for individuals who are California residents, California personal income
taxes).


General California
Municipal
MoneyMarket Fund
Annual Report
July 31, 1994

GENERAL CALIFORNIA MUNICIPAL
MONEY MARKET FUND
144 Glenn Curtiss Boulevard
Uniondale, NY 11556
MANAGER
The Dreyfus Corporation
200 Park Avenue
New York, NY 10166
CUSTODIAN
The Bank of New York
90 Washington Street
New York, NY 10286
TRANSFER AGENT &
DIVIDEND DISBURSING AGENT
The Shareholder Services Group, Inc.
P.O. Box 9671
Providence, RI 02940




Further information is contained in the Prospectus,
which must precede or accompany this report.












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